Задача 2: аппроксимация функции

In [1]:

    

from math import sin, exp


    

In [2]:

    

def func(x):
    return sin(x / 5.) * exp(x / 10.) + 5. * exp(-x / 2.)


    

In [3]:

    

import numpy as np
from scipy import linalg


    

In [4]:

    

arrCoordinates = np.arange(1., 15.1, 0.1)
arrFunction = np.array([func(coordinate) for coordinate in arrCoordinates])


    

In [5]:

    

#многочлен первой степени
arrCoord1 = np.array([1, 15])
N = 2
arrA1 = np.empty((0, N))
for i in xrange(N):
    arrA1Line = list()
    for j in xrange(N):
        arrA1Line.append(arrCoord1[i] ** j)
    arrA1 = np.append(arrA1, np.array([arrA1Line]), axis = 0)

arrB1 = np.array([func(coordinate) for coordinate in arrCoord1])

print arrCoord1
print arrA1
print arrB1


    

    




[ 1 15]
[[  1.   1.]
 [  1.  15.]]
[ 3.25221687  0.63522142]

In [6]:

    

arrX1 = linalg.solve(arrA1, arrB1)
print arrX1


    

    




[ 3.43914511 -0.18692825]

In [7]:

    

def func1(x): return arrX1[0] + arrX1[1] * x
arrFunc1 = np.array([func1(coordinate) for coordinate in arrCoordinates])


    

In [2]:

    

%matplotlib inline
import matplotlib.pylab as plt


    

In [3]:

    

plt.plot(arrCoordinates, arrFunction, arrCoordinates, arrFunc1)
plt.show()


    

    




---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-3-afbc242dad83> in <module>()
----> 1 plt.plot(arrCoordinates, arrFunction, arrCoordinates, arrFunc1)
      2 plt.show()

NameError: name 'arrCoordinates' is not defined

In [10]:

    

#многочлен второй степени
arrCoord2 = np.array([1, 8, 15])
N = 3
arrA2 = np.empty((0, N))
for i in xrange(N):
    arrA2Line = list()
    for j in xrange(N):
        arrA2Line.append(arrCoord2[i] ** j)
    arrA2 = np.append(arrA2, np.array([arrA2Line]), axis = 0)
    
arrB2 = np.array([func(coordinate) for coordinate in arrCoord2])

print arrCoord2
print arrA2
print arrB2


    

    




[ 1  8 15]
[[   1.    1.    1.]
 [   1.    8.   64.]
 [   1.   15.  225.]]
[ 3.25221687  2.31617016  0.63522142]

In [11]:

    

arrX2 = linalg.solve(arrA2, arrB2)
print arrX2


    

    




[ 3.32512949 -0.06531159 -0.00760104]

In [12]:

    

def func2(x): return arrX2[0] + arrX2[1] * x + arrX2[2] * (x ** 2)
arrFunc2 = np.array([func2(coordinate) for coordinate in arrCoordinates])


    

In [13]:

    

plt.plot(arrCoordinates, arrFunction, arrCoordinates, arrFunc1, arrCoordinates, arrFunc2)
plt.show()


    

In [14]:

    

#многочлен третьей степени
arrCoord3 = np.array([1, 4, 10, 15])
N = 4
arrA3 = np.empty((0, N))
for i in xrange(N):
    arrA3Line = list()
    for j in xrange(N):
        arrA3Line.append(arrCoord3[i] ** j)
    arrA3 = np.append(arrA3, np.array([arrA3Line]), axis = 0)
    
arrB3 = np.array([func(coordinate) for coordinate in arrCoord3])

print arrCoord3
print arrA3
print arrB3


    

    




[ 1  4 10 15]
[[  1.00000000e+00   1.00000000e+00   1.00000000e+00   1.00000000e+00]
 [  1.00000000e+00   4.00000000e+00   1.60000000e+01   6.40000000e+01]
 [  1.00000000e+00   1.00000000e+01   1.00000000e+02   1.00000000e+03]
 [  1.00000000e+00   1.50000000e+01   2.25000000e+02   3.37500000e+03]]
[ 3.25221687  1.74684595  2.50541641  0.63522142]

In [15]:

    

arrX3 = linalg.solve(arrA3, arrB3)
print arrX3


    

    




[ 4.36264154 -1.29552587  0.19333685 -0.00823565]

In [16]:

    

def func3(x): return arrX3[0] + arrX3[1] * x + arrX3[2] * (x ** 2) + arrX3[3] * (x ** 3)
arrFunc3 = np.array([func3(coordinate) for coordinate in arrCoordinates])


    

In [17]:

    

plt.plot(arrCoordinates, arrFunction, arrCoordinates, arrFunc1, arrCoordinates, arrFunc2, arrCoordinates, arrFunc3)
plt.show()


    

In [18]:

    

with open('answer2.txt', 'w') as fileAnswer:
    for item in arrX3:
        fileAnswer.write(str(item) + ' ')


    

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